This invention relates to an electromagnetic flowmeter capable of accurately measuring the flow rate of a fluid passing through a circular conduit regardless of the flow velocity distribution of the fluid.
In conventional electromagnetic flowmeters, efforts have been made to provide a uniform exciting field to improve the measurement accuracy. Such a uniform exciting field can only improve the measuring accuracy, however, when the flow velocity distribution of the fluid is symmetrical with respect to the center axis of the tube or conduit, and if the distribution is not symmetrical considerable error results even if the magnetic field is completely uniform.
Referring to FIG. 4, it is assumed that the Z axis represents the flow direction of a fluid to be measured passing through a conduit G, the Y axis represents the direction connecting electrodes A.sub.1 and A.sub.2, the X axis represents the direction along which an exciting magnetic field B is applied perpendicular to both the Y and Z axes, Vz represents the flow velocity at an arbitrary point L (x, y), and the conduit G is a cylindrical body having a radius of a and covered with insulating material on its inner surface. Since the exciting magnetic field can be regarded as constant over a minor length of the Z axis, the consideration can be restricted only to two dimensional changes with respect to the components Bx and By in the directions of the X and Y axes. The voltage e generated between the electrodes A.sub.1 and A.sub.2 is represented by the equation: ##EQU1## WHERE F is a cross-section of the conduit G including the electrodes A.sub.1 and A.sub.2, Vz is the flow rate at an arbitrary point L (x, y) in the electrode-containing cross-section F, and Wx and Wy are "weighted functions" which represent the contributions of the X and Y components to the unit electromotive force generated at the arbitrary point L (x, y) in the electrode-containing cross-section F, or to the output signal generated between the electrodes A.sub.1 and A.sub.2, and which are determined only by the geometrical structure of the conduit G and the electrodes A.sub.1 and A.sub.2 regardless of the magnetic field distribution and the flow velocity distribution. It is known from the studies of J. A. Shercliff that the Y-component Wy has a distribution as shown in FIG. 5.
Since the exciting magnetic field B in conventional electromagnetic flowmeters is uniform, and therefore the X-component Bx and the Y-component By are, theoretically, Bx = constant and By = 0, equation (50) may be rewritten as: ##EQU2## Since the weighted function Wy in equation (51) has different values depending on cross-sectional position, as shown in FIG. 5, the output signal e includes errors unless the flow velocity distribution at each point L (s, y) within the conduit G is symmetrical with respect to the center axis Z. It can be confirmed by the transformation of equation (51) that if the distribution is symmetrical the effect of the weighted function is eliminated.
Based on the result of Shercliff's studies, it was proposed in DAS No. 1,295,223 to establish the magnetic field Bx for each point L (x, y) within the conduit cross-section in inverse proportion to the weighted function, as shown in equation (52), to thereby eliminate the adverse effects of the flow velocity distribution. ##EQU3##
The theoretical basis of DAS No. 1,295,223 rests on the assumption that the electrodes A.sub.1 and A.sub.2 are infinitely small, that is, in the form of point electrodes. Since most flowmeter electrodes have a diameter of about 6-10 (mm) however, the theory represented by equation (52) is not always valid, and errors are produced in the output signal.